Please solve my question

stevengoh911 · July 10th 2007, 07:08 AM

Given
x,y ∈ [0,2c]
f(x),g(y) ∈ [0,2c]
Show
| xy-f(x)-g(y)|≥ c²
exist

I don't really get this question.
Please help me

**ThePerfectHacker** · July 10th 2007, 09:37 AM

Originally Posted by stevengoh911

Given
x,y ∈ [0,2c]
f(x),g(y) ∈ [0,2c]
Show
| xy-f(x)-g(y)|≥ c²
exist

It is assumed that $c>0$ :

Consider the points $(0,2c),(2c,0),(0,0)$ if these work then we are finished. Otherwise,
$|f(0)+g(0)|<c^2$
$|f(2c)+g(0)|<c^2$
$|f(0)+g(2c)|<c^2$

Now, the claim is that $|f(2c)+g(2c)-4c^2|\geq c^2$ .
This is true because,
$f(2c)+g(2c) = [f(2c)+g(0)] + [f(0)+g(2c)] - [f(0)+g(0)] < c^2+c^2+c^2 = 3c^2$
But then,
$f(2c)+g(2c) - (2c)(2c) < 3c^2 - (2c)(2c) = -c^2$
Thus,
$|f(2c)+g(2c) - (2c)(2c)|\leq c^2$

Thread: Please solve my question

LinkBack

Thread Tools

Display

Please solve my question

Similar Math Help Forum Discussions

How to solve this question with a ti-89

how should i solve this question?

I'm not sure how to solve this question?

How I can solve this question

How should I solve this question?

Search Tags